I I

No. 13557

FINITE ELEMENT ANALYSIS

OF THE ARMORED VEHICLE LAUNCHED BRIDGE (AVLB)

MARCH 1992

Roberto P. GarciaStephen G. LambrechtU.S. Army Tank-Automotive CommandATTN: AMSTA-RYC

By Warren. MI 48397-5000

APPROVED FOR PUBLIC RELEASE:DISTRIBUTION IS UNLIMITED 00o3/ I)LI,# 60t3

U.S. ARMY TANK-AUTOMOTIVE COMMANDRESEARCH, DEVELOPMENT & ENGINEERING CENTERWarren, Michigan 48397-5000

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

1 13 March 1992 Final, May 1991 - Dec 19914. TITLE AND SUBTITLE S. FUNDING NUMBERS

inite Element Analysis of the Armored Vehicle Launchedridge (AVLB)

6. AUTHOR(S)

oberto P. Garciatephen G. Lambrecht

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) S. PERFORMING ORGANIZATION

REPORT NUMBER

U.S. Army Tank-Automotive Command

STA-RYC 13557

Jarren, II 48397-5000

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11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/ AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Approved for Public Release:

Distribution is Unlimited

13. ABSTRACT (Maximum 200 words)

The Armored Vehicle Launched Bridge (AVLB) is a folding bridge that was fielded

in the early 1960's as the Army's standard heavy assault bridge. The bridge is

rated for normal crossings of military load classifiecation of 60 tons (MLC 60)

over a maximum gap of 60 feet and a vehicle speed of 25 mph. The System Simulation

and Technology Division, AMSTA-RY, was tasked by the Systems EngineeringDirectorate, AMSTA-U, to perform an anlaysis of the AVLB over a 60-foot gap while

an MIAI crosses it. The objective of this project was to perform a finite element

analysis (FEA) of the whole AVLB to determine high-stress areas of concern.

14. SUBJECT TERMS 15. NUMBER OF PAGES55

Finite Element Analysis, AVLB 16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT

OF REPORT OF THIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified SAR

TABLE OF CONTENTS

Section Page

1.0. INTRODUCTION ............... ................. 5

2.0. OBJECTIVE .................. ................... 5

3.0. CONCLUSIONS ................ .................. 5

4.0. RECOMMENDATIONS ................... ......... 7

5.0. DISCUSSION ................. .................. 75.1. A. .. roach *.............. .................. 75.2. Finite Element Method ........ ... ............ 85.3. Computer Software and Hardware ....... ........ 85.3.1. PATRAN ................... .................... 85.3.2. ABAQUS ................... .................... 85.4. Finite Element Models ........... ............ 85.4.1. Beam model ................. .................. 95.4.2. Plate model ................ ................. 95.4.3. Materials ................. .................. 95.4.4. Added masses ........... ................. 135.4.5. Boundary conditions ........ ............. 135.5. Discussion of Results ...... ............ 145.5.1 Eigenvalues ............ ................. 145.5.2. Gravity load ........... ................. 155.5.3. Static vehicle ........... ................ 155.5.4. Moving vehicle ........... ................ 155.5.5. Additional analyses ........ ............. 22

APPENDIX A, AVLB Materials and Properties ... ....... .. A-1

APPENDIX B, Result plots of AVLB plate Model Analysis . B-i

APPENDIX C, ABAQUS Input File of AVLB Beam Model . . . C-1

DISTRIBUTION LIST .......... ................. Dist-1

2

LIST OF ILLUSTRATIONS

Figure Title Page

1-1. Armored Vehicle Launched Bridge ......... .......... 6

5-1. Beam Finite Element Model of AVLB ....... ......... 10

5-2. Plate Finite Element Model of AVLB .... ........ 11

5-3. Under Side View of Plate Finite Element Model . 12

5-4. Von Mises Stress with Gravity Only .... ........ 16

5-5. Von Mises Stress with MIAl Parked Over Center . . 17

5-6. Close-up of Right Hinge Showing Von Mises Stress . 18

5-7. Total Elastic Strains with MlAl Parked Over Center . 19

5-8. Von Mises Stress with MIAl at Quarter Span ....... .. 20

5-9. Von Mises Stress with MlAI at Center ... ........ .. 21

5-10. Shear Stress with MIAl Parked Over Center .. ..... .. 23

5-11. Fracture During Actual AVLB Testing ..... ........ 24

5-12. Von Mises Stress with Modified Hinge Area .. ..... .. 25

3

LIST OF TABLES

Table Title Page

3-1. Summary of Plate Finite Element Analysis Results 7

5-1. Properties of Two Materials on Bridge ... ....... .. 13

5-2. Nonstructural Items Added to Models as Mass Loads 13

5-3. AVLB Beam Model Eigenvalue Results .... ........ .. 14

5-4. Summary of Plate Finite Element Analysis Results . 22

4

1.0. INTRODUCTION

The Armored Vehicle Launched Bridge (AVLB) is a folding bridgethat was fielded in the early 1960s as the Army's standard heavyassault bridge. Fielded versions include both the M60 and M48tank chassis. The bridge is constructed primarily of aluminumalloy and weighs approximately 29,500 lbs. FIGURE 1-1 depictsthe deployed AVLB during strain gage testing.

The bridge is rated for normal crossings of military loadclassifications of 60 tons (MLC 60) over a maximum gap of 60feet and a vehicle speed of 25 mph. MLC 61-64 loads at 8 mphare classified as caution crossings, and MLC 65-75 at 3 mph areclassified as risk crossings for the same gap distance. Thefielding of the MIA1 Abrams main battle tank with the T-158track has resulted in a load classification of MLC 68, which isa risk category for crossing the AVLB.

The System Simulation and Technology Division, AMSTA-RY, wastasked by the Systems Engineering Directorate, AMSTA-U, toperform an analysis of the AVLB over a 60-foot gap while an MlAlcrosses it. The Analytical and Physical Simulation Branch,AMSTA-RYA, performed the flexible body dynamic analysis portionof this project, and the Computer-Aided Engineering Branch,AMSTA-RYC, performed the quasi-static finite element analysis.This report covers the finite element analysis aspect.

2.0. OBJECTIVE

The objective of this project was to perform a finite elementanalysis of the whole AVLB to determine high-stress areas ofconcern. A low-resolution beam Finite Element Model (FEM) ofthe AVLB was created first, in order to obtain certain modalcharacteristics of the bridge. The information from the beammodel was used by Dr. Roger A. Wehage and Mr. Micheal J.Belczynski of AMSTA-RYA to create a Symbolically OptimizedVehicle Analysis System (SOVAS) model of the AVLB to interactwith a current MIAl model. These mathematical models were usedto determine distributed vehicle dynamic reaction loads on thewhole AVLB. Time histories of all forces and moments from thedynamic analysis were used as inputs to a higher resolutionplate finite element model of AVLB. Several different finiteelement analyses were performed for the purpose of locatingpotential high-stress areas.

3.0. CONCLUSIONS

The results of this report are based on a bridge in "like newcondition" with no rust or other damage. Also, no fatigueanalysis or prototype tests were performed for this project. Nomud loads or steering corrections were applied to the bridge andthe ends were level and simply supported.

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The area just above the center hinges consistently had thehighest stresses. On the analyses that simulated the MlAldirectly over the center of the bridge, the von Mises stresseswere considerably greater than the ultimate strength of thematerial, indicating a structural failure near this location.The speed of the vehicle did not seem to have an effect on themagnitude of the stress; however, with increased speeds, thebridge seemed to sway more from side to side. TABLE 3-1 belowsummarizes the results from this project. These values werecompared to the yield strength of 2014-T6 aluminum which is 60.2ksi.

Analysis Von Mises Stress Max. DisplacementGravity 12,469 psi 1.245 in.Static (68.2 ton) 119,119 psi 10.80 in.3mph (Quarter span) 58,480 psi 5.936 in.3mph (Center) 119,234 psi 10.82 in.8mph (Quarter Span) 66,663 psi 6.820 in.8mph (Center) 118,169 psi 10.70 in.25mph (Quarter Span) 61,566 psi 6.101 in.25mph (Center) 118,993 psi 10.64 in.

TABLE 3-1. Summary of Plate Finite Element Analysis Results.

4.0. RECOMMENDATIONS

It is recommended that a more detailed model, perhaps a 3-Dsolid model, of the center hinge and surrounding area be createdand a finite element analysis be performed. This analysis wouldfurther pinpoint the critical location and would better quantifythe stress results. It was found that this hinge location isthe only real area of concern on the bridge. This location mayhave to be redesigned or modified on the actual AVLB, in orderto support the increased vehicle loads.

5.0. DISCUSSION

5.1. ADproach

The technical approach used for this project was based on theutilization of computer-aided simulation and finite elementanalysis methods. This project used a three-step process.First, a low-resolution beam finite element model of the bridgewas created in order to obtain certain modal characteristics ofthe bridge quickly. This information was then used by AMSTA-RYAto create a model of the bridge in their SOVAS package. They,in turn, performed a number of dynamic runs simulating a 68.2-ton MlAl driving down the center line of the AVLB with nosteering corrections at three different vehicle speeds; 3 mph, 8mph, and 25 mph. These runs resulted in a set of force loadingsfor each.

7

During the time taken to perform the dynamic simulations, a moredetailed plate model of the bridge was created. The forceloadings for the different speeds were then applied to thisplate model to determine the critical stresses, strains, anddeflections, while pinpointing areas of concern.

5.2. Finite Element Method

The finite element method is an analysis technique for solvingthe differential equations of complex problems. This method hasbecome a valuable tool for modeling structural, mechanical,thermal, and fluid systems. In finite element analysis, astructure is broken down into simple discrete regions, or finiteelements. These simple structural elements, which can be beams,shells, or solids, have elastic behavior that can be formulatedmathematically. These elements are then assembled to form theoverall structure of the item being analyzed. It is mandatorythat the behavior of the model closely exhibits the behavior ofthe actual physical structure, in order to obtain realisticresults and verify the model.

5.3. Computer Software and Hardware

5.3.1. PATRAN. PATRAN is a pre/postprocessing software packagedeveloped by PDA Engineering. PATRAN is used to visually createthe FEM. PATRAN's postprocessor allows the analyst to view theresults of the analysis in graphical form. PATRAN resides on aVAX 8800 and viewed using Tektronix terminals. PATRAN is alsoon a Silicon Graphics Personal Iris workstation.

5.3.2. ABAQUS. ABAQUS is a large-scale, general-purpose finiteelement analysis program capable of analyzing complexstructures. The analyst first needs an input file, which inthis case was created using PATRAN. The input file defines theshape and material properties of the model, as well as boundaryconditions and loads. The program then assembles and solves asystem of equations on TACOM's Cray-2 Supercomputer and outputsthe results. ABAQUS was developed by Hibbitt, Karlsson, &Sorensen, Inc.

5.4. Finite Element Models

The finite element model contains all the information needed torun the analysis. The model defines the actual shape anddimensions of the bridge, the materials used and theirproperties, and any boundary conditions and force loadings.

The models were constructed using PATRAN. Using grids, lines,and patches, the geometry of the bridge was created first. Thefinite elements and corresponding nodal points were then made

8

using the geometry. The materials were defined along with theelement thicknesses and boundary conditions. This PATRAN modelwas then translated into an ABAQUS input model using atranslator called PATABA. The force loadings and masses wereadded to the ABAQUS input file using the vi editor on the Cray-2super computer. Two finite element models were created for thisproject-- a low-resolution beam model and a more detailed platemodel.

5.4.1. Beam model. This low-resolution, three-dimensional (3-D) model is composed of 2-D B3 ABAQUS beam elements. The modelhas 228 nodes, 252 beam type elements, and 1912 degrees offreedom (DOF). See FIGURE 5-1. With beam elements, the crosssection of each element was defined in ABAQUS. This beam modelwas used to obtain certain modal characteristics of the bridgequickly. Such characteristics include: eigenvalues andeigenvectors, the stiffness matrix, and nodal generalizedmasses, which were obtained after performing ar analysis for thefirst six mode shapes. This information was used by AMSTA-RYAto develop the dynamic modal representation of the bridgesuitable for interacting with the MlAl vehicle model. Acomplete listing of the ABAQUS input file for this beam model islocated in Appendix C.

5.4.2. Plate model. Although the beam model is a goodrepresentation of the bridge giving good results, it is notdetailed enough to pinpoint areas of concern. It is for thisreason a more detailed plate model of the AVLB was created.This model is composed of 37,250 shell elements, the majority ofwhich are quad type, and 18,780 nodes. None of the rivets weremodeled for this project. The entire bridge was modeled; nosymmetry was used, since the loadings were not symmetrical.FIGURE 5-2 depicts the AVLB plate model, and FIGURE 5-3 showsthe plate model viewed from the underside.

The plate model is constructed of SR4 quad/4 elements and STRI3tri/3 elements. The quad/4 elements have four nodes, one ateach of the corners, and the tri/3 elements have 3 nodes. Theseshell elements have six degrees of freedom, giving the entiremodel 112,680 degrees of freedom. The STRI3 elements are flatfaceted elements, which were used since the AVLB model has nocurved or rounded surfaces. With shell elements, the thicknessof each element needed to be given. This model has twenty-four(24) different properties, or thicknesses defined.

5.4.3. Materials. There are a number of different types ofmaterials on the AVLB, but only two classes: steel and aluminum.On the two finite element models, the density, Modulus ofElasticity, and Poison's Ratio are the same for all thematerials in their class. Therefore, only two classes ofmaterials are defined, steel and aluminum. See TABLE 5-1. Itis not until the results are being interpreted that the actualspecific material with its yield, ultimate, and shear strengthsis compared. See Appendix A for a complete list of materialtypes on the AVLB, along with their properties.

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Modulus of Elasticity 10.6 x 106 psi 29.0 x 106 psiUltimate Tensile Strength 70.1 ksi 58.0 ksiYield Strength 60.2 ksi 36.0 ksiShear Strength 42.1 ksi 21.0 ksiDensity 0.101 lb/in3 0.284 lb/in3

Poison's Ratio 0.34 0.31

TABLE 5-1. Properties of Two Materials on Bridge1 .

5.4.4. Added masses. On both the beam model and plate modelcertain items were not physically modeled, because they did notadd to the structural integrity of the AVLB. TABLE 5-2 liststhese items along with their actual weights. However, theweight of the finite element model must be the same as that ofthe actual AVLB, in order to determine the correct modalinformation and to include the gravity effects. The cylinderand quadrant were added at their respective locations on thebridge models as mass loads. An analysis simulating gravityacting on the bridge was performed, and the weight of the modelwas found to be 25,824.3 lb. The actual weight of the AVLB is29,500 lb. The difference was then distributed as a mass loadover the entire bridge model.

Item WeiahtCylinder 1500 lbsQuadrant 500 lbsCables 100 lbs ea.Cable Ends 60 lbs ea.Side Curbs 1800 lbsCylinder Braces 60 lbsLaunch Tongue 240 lbsQuadrant Bracket 100 lbsBeams for Cable Ends 250 lbs

TABLE 5-2. Nonstructural Items Added to Models as Mass Loads.

5.4.5. Boundary conditions. Both of the bridge models wereconstrained to simulate a 60-ft span or crossing distance. Onthe plate model, it actually was 59.81 ft. because of nodelocations. On both FEA models, the leading edge of the bridgeis constrained from moving vertically, laterally, andlongitudinally, while the trailing edge is constrained frommoving vertically only. This boundary condition closelysimulates the true condition, while also satisfying the type ofconstraints needed for the analysis code.

IBeer, F. P. and E. R. Johnston, Jr., Mechanics ofMaterials, McGraw-Hill Book Company, 1981, p. 584

13

For the plate model, special constraints were needed to simulatethe hinges and pinned locations of the AVLB. ABAQUS' Multi-Point Constraint (MPC) number 9 provides a pinned jointbetween two nodes. This makes the displacements equal butleaves the rotations, if they exist, independent of each other.This MPC number 9 was used at 24 locations on the bridge model.

5.5. Discussion of Results

The Finite Element Analysis (FEA) was run using ABAQUS on aCray-2 Supercomputer. A quasi-static analysis type was used forthis project, since it includes the effects of gravity. Theanalysis for the AVLB plate model had an average run wall clocktime of about three hours. The results file from the analysiswas then translated into a format that PATRAN can read using aproduct known as ABAPAT. The results are displayed andinterpreted in PATRAN. PATRAN allows the analyst to visuallydisplay analysis results.

The Maximum Distortion Energy criterion was used to quantify theresults for this project. According to this criterion, alsoknown as the von Mises criterion, a given structural componentis safe, as long as the maximum value of the distortion energyper unit volume in that material remains smaller than thedistortion energy per unit volume required to cause yield in atensile test specimen of the same material. For this project,the von Mises stress, which also takes into account the sheareffects, was compared to the yield strength of the material.

The results from each analysis are discussed in the followingsections. A summary of the results for the plate model are inTABLE 5-4.

5.5.1. Eigenvalues. The first analysis was an eigenvectoranalysis performed on the beam model, which gave the first sixmodal equations of motion. This analysis was performed toobtain certain properties of the bridge, in order for AMSTA-RYAto create the SOVAS model. The results and information fromthis analysis are listed in TABLE 5-3 below. It was laterdetermined that the first five mode shapes were sufficient torepresent the most significant bridge deflections under vehicleloading.

Mode Shape Eiaenvalue Freauencv1 63.302 1.2663 Hz2 805.56 4.5172 Hz3 987.88 5.0023 Hz4 2721.7 8.3032 Hz5 3242.5 9.0627 Hz6 4006.5 10.074 Hz

TABLE 5-3. AVLB Beam Model Eigenvalue Results.

14

5.5.2. Gravity load. The first analysis performed on the platemodel simulated the AVLB at a 60-ft span with only gravityacting on it. Not only did this give some results such asmaximum deflection and stress, but it also checked for anyerrors in the finite element model and ABAQUS input file. Asexpected, the results were symmetric about the longitudinalcenter line. The von Mises stress for this loading was 12,469psi, and the maximum deflection was 1.245 inches. As would beexpected, the maximum stress is well below the yield strength ofthe material. FIGURE 5-4 is the von Mises stress plot for thisloading. The bridge is viewed from the under-side in this plot,so that all the hinges are visible. The highest stress occurredjust above the center hinges. In fact, in all of the stressplots for this project, the highest stress occurred at thislocation.

5.5.3. Static vehicle. The next type of analysis simulated a68.2-ton MIAl parked directly over the center of the AVLB. Theforce loadings were taken from the SOVAS dynamic analysis of theMIAl at 3 mph when located directly over the center of thebridge. The longitudinal and lateral force components, x and zrespectfully, were removed leaving only the vertical forces.The von Mises stress from this condition was 119,119 psi, andthe maximum deflection was 10.80 inches. This high stressindicates a failed condition. As can be seen in FIGURE 5-5, thestresses are higher toward the right side of the bridge. Thiscan be accredited to the fact that the forces used were from the3 mph dynamic analysis, and the bridge seemed to sway side toside when the vehicle is moving over the AVLB. The time periodused here indicates the bridge was swaying toward the right.FIGURE 5-6 is a close-up of the right hinge, better showing thestress concentration.

As a model verification, the total elastic strains in thelongitudinal direction were compared to strain gage data from anactual test at Ft. Belvoir. The strain values were of the samemagnitude and within the same range. FIGURE 5-7 is a plot ofthe total elastic strains from this analysis. There was nospecific test data for a 68.2-ton load, so an interpolation wasmade between bordering loads. Ft. Belvoir's Bridge Divisiontesting results range from 1289 -gstrain to 1875 ttstrain. Theanalysis strain in the same location are in the range of 1240gstrain to 1830 Istrain.

5.5.4. Moving vehicle. For the analyses of the differentvehicle speeds; 3 mph, 8 mph, and 25 mph, a quasi-static finiteelement analysis was performed using ABAQUS. The loads used arefrom the dynamic simulation of that speed at a particular timeinterval. Two different time periods were chosen for eachspeed-- when the MlAI was directly over the center of the bridgeand half way between the beginning and the center (quarterspan). The stresses were consistently higher for all speedswhen the vehicle was at the center. The speed of the vehicledid not seem to have an effect on the magnitude of the stress or

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the deflection. The speed did seem to effect the swaying of thebridge, which may have some fatigue effects on the life of theAVLB. This sway is especially noticeable on the 25 mphanalysis. On the stress plot at quarter span, FIGURE 5-8, thestresses are higher toward the left side of the bridge. Then onthe 25 mph plot with the vehicle at the center, FIGURE 5-9, thestresses are higher towards the right side.

Analysis Von Mises Stress Max. DisplacementGravity 12,469 psi 1.245 in.Static (68.2 ton) 119,119 psi 10.80 in.3mph (Quarter span) 58,480 psi 5.936 in.3mph (Center) 119,234 psi 10.82 in.8mph (Quarter Span) 66,663 psi 6.820 in.8mph (Center) 118,169 psi 10.70 in.25mph (Quarter Span) 61,566 psi 6.101 in.25mph (Center) 118,993 psi 10.64 in.

TABLE 5-4. Summary of Plate Finite Element Analysis Results.

The location just above the hinges always had the highest stressvalue at all speeds and all vehicle locations. Most of thisstress is shear in the x-y plane, as can be seen in FIGURE 5-10.In actuality, the stress might not be in this exact location.On the actual AVLB, the hinge is riveted on. When the AVLBfailed in actual tests, a crack appeared at the last rivetlocation on the hinge on the lower flange. See FIGURE 5-11.This analysis shows there exists a problem in this general hingelocation. A more detailed finite element model of this areawould further pinpoint the critical location.

5.5.5. Additional analyses. In order to determine if thethickness around the hinge area has any effect on the stress orits location, a final analysis was performed on the AVLB, withthe vehicle at the center and a speed of 8 mph. The thicknessof one of the hinges at the location of the high stress wasincreased from 0.375 inches to 1.125 inches. As can be seen inthe von Mises stress plot in FIGURE 5-12., the stressconcentration is still in the same location; however themagnitude decreased, by about 50 ksi, to the value of 62 ksi.This is just above the yield strength of the 2014-T6 aluminummaterial.

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APPENDIX A

AVTB Materials and Properties

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ALUMINUM ALLOYS

StrenathsDesignation Density Ultimate Yield Shear6061-T6 0.098 lb/in 3 45.0 ksi 39.9 ksi 29.7 ksi2014-T6 0.101 lb/in 3 70.1 ksi 60.2 ksi 42.1 ksi

FERROUS METALS

StrenqthsDesiqnation Density Ultimate Yield ShearASTM A108 0.284 lb/in 3 55.0 ksi 30.0 ksiASTM A120 0.284 lb/in 3

ASTM A36 0.284 lb/in 3 58.0 ksi 36.0 ksi 21.0 ksiASTM A441 0.284 lb/in 3 60-70 ksi 40-50 ksiASTM A575 0.284 lb/in 3

ASTM A514 0.284 lb/in 3 120 ksi 100 ksi 55 ksi

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APPENDIX B

Result Plots of AVLB Plate Model Analysis

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APPENDIX C

ABAQUS Input File of AVLB Beam Model

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m aC)+++) C)+++a++C+++4C C a ++3+C+C a+D+>+mC +++ ++aa a-++++aC) +++C+C+a+a ++) a ++a ++ CDC)a C+a0+C++a+aQ+o ............................ i ...........................LUULUULLJULUULUULUULULULLULu) 000000000O0000000O00000Iu0000W0OO00000w 00wW 00WW0W0000000wUj i LUW Ww j L w W 'U sJ . Jiu s ' W

a - C)C>0000O0>0C 00C C C 00C>CDC3C>C0CD00000D 000CDa000C0C0C0C0C C C3CDC0C)C3000CD00C3C000CD 0 C -Mcl l M" - ~ la0C0C0C0aC0C00>C>010C0C00000C0aCDCDa 00CD03CD0000aCDCD0D00CDC>0Da000Q000>00000D030D0C0C0ma 0It* t 0000000ta- aoooCooC>ooooaaooooCoMaoooo aC>C)0 Doo CDCDCDo DC>o )aoooooCoCoaoD ooooC 0CDC3CDoo0o3oooDCDaoaC3CD C C

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0000000000000000000000000000000000 14 ý -44- ýAi -- 4 100000000000000000a ýr* -t-I %r 00000 41-.0. . . . . . . . . . . . . . . . . . . .

C) CD 00000a0( 3 )aaC DC)aCOaaC 1 3C 0C ý DC .C C DC 0 CC)DCDýa 3DaCDCD aCD CD CD0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0

0 o 0 0 toto r - - -to oto 0to 0 oto 00( o 0 C wto w 0to wwto towto 000 aa 00a0N"0000"0"" aC% aCD ""0) DmnaC o o o0omoomCoaoooooma oo aooo3o3 ooo3oDo3 ooooCDooa D C C)0 ooooaCDM--ooo- oo4 D D-34( C-C - - 4m DM. O 50jC OtOtoO O LotO O totLOO4 )C )LO DOOOOOOOOCDOOaOOaCo C ýC DmC )C 3C ýC DC 3COOaODODOOODOCOO C

tO r-. r- tl- U)c nNti"U OC o l l )f- l11L -C D0C lC DC D C\J to 0' C's Q'. CD CD C. CNI C>4 CD CDI Co CD a- C3 CD CD 000 0 0 00 0 0 0 00 0 0 00 0 0 0to- ODODO r- -- f C'' 1-4-4 -4 (N t- (0 tO tO I- Olimmmc MO to (Ni (0 W0(V W). V) LO Lo o LOa inC DCý0C an an an C>l tC tCDtCD00000000000000000000

ci 1*r It- t0cli mt ~ 4 - rI14 c. ni o a n aDc c 'acococo D o a oooo Daao a r' -- oooor-t-o ac)cDa -. rr-al r O0 D -0 )0 0(0COM0t 4-d-A't 000000DMMM MMMMM D 3 )Q Dt r- r- f- r- -i'-D000CD0CUa)U)U4m o) f-f-r%-Imto U')toto0 LtO Mto U)V) m )OU ) CA ) 0U I L L O to)toA 1tI-t - P- Q a )000000(0(CD(0- * t (tI I0(0 CO CD0000 D1- ( 'i 000000 4 e d---ý mc - * l 4cl l d *I 4 mmC)mCDC tC MC , %-f-t - o - * dd d -*t Dt

r- ; ; 00000000000000000000000000000000000000000000000000000000C;8 C C C C C;8 ; ; C 88 ; ; C 8C;Cý8 C C C CCD

Lto to to to f' to--t-- 1- t-- (0(00(0( CO OD MMMM CD CD C300~ CO NC (0- 0( "M en M o toW to k r- tf-P -fr- r- t- t- I~-I-- (00 0(0(0(0(0(0(0(0CCto -4,.4 v-.4 -4 - - --4 4 -4 r4 -4-4 -4 -4 1 -4s--4 - -4 -4,- 4,q4 s- -4 s-I -4-sI-4 .-4 -4- -4 -4 s-IA ý -4 -4

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4-- a ) )00000000>0003C0C)0 0 C 0C0 0 00 D0 ) 00D0D00000 0a ) )0C000 C000C00OC0Oý0 0C)C)0 ) C o 00 ý0 C C C C0uaLOC 0t00000tC) O000t00000000000 C )C ýL >00C >0000( DC oa00C )0C 000000C ý , )00C)00C0C000 a0 00a0 0C4J 3r f C Oaar I)C OC 0r.o t00-ot00rl-LO C D000toCý0 0 L)0 a o00 tCoC)00tO D0 00tO0C)00to) D O00tCooo0CýV)C CLnoot Doot3LO DC)L

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Commander 2Defense Technical Information CenterBuilding 5, Cameron StationATTN: DDACAlexandria, VA 22304-9990

Manager 2Defense Logistics Studies Information ExchangeATTN: AMXMC-DFort Lee, VA 23801-6044

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